Penelope utility function is U (a, b) = a+ 10b−b2, where a is the amount of apples consumed and b is the amount of bananas consumed. He has $100 income. The price of apple is $0.5 per lb. Price of banana’s though increases with its purchase. Specifically, buying, b pounds of bananas will cost Pedro b2. a. What is Penelopes optimal consumption? b. Now, he suddenly acquires an extra $100 income. How this will change his allocati
Penelope utility function is U (a, b) = a+ 10b−b2, where a is the amount of apples consumed and b is the amount of bananas consumed. He has $100 income. The price of apple is $0.5 per lb. Price of banana’s though increases with its purchase. Specifically, buying, b pounds of bananas will cost Pedro b2. a. What is Penelopes optimal consumption? b. Now, he suddenly acquires an extra $100 income. How this will change his allocati
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter20: Consumer Choice: Maximizing Utility And Behavioral Economics
Section: Chapter Questions
Problem 5WNG
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Penelope utility function is U (a, b) = a+ 10b−b2, where a is the amount of apples
consumed and b is the amount of bananas consumed. He has $100 income. The
Specifically, buying, b pounds of bananas will cost Pedro b2.
a. What is Penelopes optimal consumption?
b. Now, he suddenly acquires an extra $100 income. How this will change
his allocation?
Expert Solution
Step 1
Utility function : U (a, b) = a+ 10b−b2
Income = 100
b pounds on banana cost = b2
1 pound of banana would cost = b2/b
=> b
Therefore , Price of banana = b
Budget Constraint : Pa *a + Pb *b = Income
=> 0.5 a + b2 = 100
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